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The Dynamics of Nonlinear Reaction-Diffusion Equations with Small LȨvy Noise [electronic resource] / by Arnaud Debussche, Michael Hȵgele, Peter Imkeller.

Por: Debussche, Arnaud [author.]Colaborador(es): Hȵgele, Michael [author.] | Imkeller, Peter [author.]Tipo de material: TextoTextoSeries Lecture Notes in Mathematics, 2085Editor: Cham : Springer International Publishing : Imprint: Springer, 2013Descripción: XIV, 165 p. 9 illus., 8 illus. in color. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783319008288Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Differentiable dynamical systems | Differential equations, partial | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Dynamical Systems and Ergodic Theory | Partial Differential EquationsFormatos físicos adicionales: Sin títuloClasificación CDD: 519.2 Clasificación LoC:QA273.A1-274.9QA274-274.9Recursos en línea: de clik aquí para ver el libro electrónico
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Springer eBooksResumen: This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.
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This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

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